[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of noninteracting fermions in 1D, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. The challenges for application of our method to real electronic structure problems are discussed.

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Finding density functionals with machine learning

Data augmentation is a widely used trick when training deep neural networks: in addition to the original data, properly transformed data are also added to the training set. However, to the best of our knowledge, a clear mathematical framework to explain the performance benefits of data augmentation is not available. In this paper, we develop such a theoretical framework. We show data augmentation is equivalent to an averaging operation over the orbits of a certain group that keeps the data distribution approximately invariant. We prove that it leads to variance reduction. We study empirical risk minimization, and the examples of exponential families, linear regression, and certain two-layer neural networks. We also discuss how data augmentation could be used in problems with symmetry where other approaches are prevalent, such as in cryo-electron microscopy (cryo-EM).

A Group-Theoretic Framework for Data Augmentation

The relationship between material properties and independent variables such as temperature, external field, or time is usually represented by a curve or surface in a multidimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging-based model. These include one-dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in three-dimensional space and the fitted intermolecular potential for Ar-SH, and a four-dimensional data set of experimental measurements for ${\mathrm{BaTiO}}_{3}$-based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the tradeoff methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise, as well as the budget.

Efficient estimation of material property curves and surfaces via active learning

Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic an experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.

Machine Learning for Quantum Matter

A machine-learning approach that we term the ``stochastic replica voting machine'' (SRVM) algorithm is presented and applied to a binary and a three-class classification problem in materials science. Here, we employ SRVM to predict candidate compounds capable of forming stable perovskites and double perovskites and further classify binary ($AB$) solids. The results of our binary and ternary classifications compared well to those obtained by SVM and neural network algorithms.

Stochastic replica voting machine prediction of stable cubic and double perovskite materials and binary alloys

A machine learning approach that we term that the Stochastic Replica Voting Machine (SRVM) algorithm is presented and applied to a binary and a 3-class classification problems in materials science. Here, we employ SRVM to predict candidate compounds capable of forming cubic Perovskite (ABX3) structure and further classify binary (AB) solids. The results of our binary and ternary classifications compared to those obtained by the SVM algorithm.

Stochastic Replica Voting Machine prediction of stable Perovskite and binary alloys

Graphs are useful in analysing histopathological images as they are able to represent neighbourhood interactions and spatial relationships. Typically graph nodes represent cells and the vertices are constructed by applying a nearest neighbor algorithm to cell’s locations. When passing these graphs through one graph neural network (GNN) message passing step, each node can only utilise features from nodes within its immediate neighbourhood to make a classification. To overcome this, we introduce two levels of hierarchically connected nodes that we term “supernodes”. These supernodes, used in conjunction with at least four GNN message passing steps, allow for cell node classifications to be influenced by a wider area, enabling the entire graph to learn tissue-level structures. The method is evaluated on a supervised task to classify individual cells as belonging to a specific tissue class. Results demonstrate that the inclusion of supernodes with multiple GNN message passing steps increases model accuracy. 

Using Hierarchically Connected Nodes and Multiple GNN Message Passing Steps to Increase the Contextual Information in Cell-Graph Classification

A machine learning approach that we term the `Stochastic Replica Voting Machine' (SRVM) algorithm is presented and applied to a binary and a 3-class classification problems in materials science. Here, we employ SRVM to predict candidate compounds capable of forming stable perovskites and double perovskites and further classify binary ($AB$) solids. The results of our binary and ternary classifications compared well to those obtained by SVM and neural network algorithms.

Stochastic Replica Voting Machine Prediction of Stable Cubic and Double Perovskite Materials and Binary Alloys

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Stochastic replica voting machine prediction of stable cubic and double perovskite materials and binary alloys

Stochastic Replica Voting Machine prediction of stable Perovskite and binary alloys

Using Hierarchically Connected Nodes and Multiple GNN Message Passing Steps to Increase the Contextual Information in Cell-Graph Classification

Stochastic Replica Voting Machine Prediction of Stable Cubic and Double Perovskite Materials and Binary Alloys